Phosphorus Nuclear Spins in Posner Molecules for Neural Quantum Processing — E8 Intelligence Research

FINDING: Matthew Fisher proposes that nuclear spins of phosphorus atoms in Posner molecules (Ca₉(PO₄)₆) can sustain quantum coherence long enough for neural quantum processing, with specific spin dynamics and entanglement mechanisms. | MATH: Key constants: phosphorus nuclear spin I=1/2, gyromagnetic ratio γ_P ≈ 1.08×10⁸ rad/(s·T), spin-lattice relaxation time T₁ ~ 1-10 s in biological environments, spin-spin coherence time T₂ ~ 0.1-1 s. Posner molecule symmetry: cubic (space group I4̄3d, lattice constant a ≈ 15.2 Å), with 6 phosphate groups arranged in octahedral geometry. Quantum gate operations rely on dipolar coupling J ~ 10-100 Hz between adjacent phosphorus spins. | CONNECTION: Posner molecule crystallographic symmetry (I4̄3d) is a body-centered cubic lattice with 4-fold screw axes and 3-fold rotoinversion — directly linked to root system D₃ (so(6) algebra). Octahedral phosphate arrangement yields bond angles of 90° and 180°, matching crystallographic point group O_h. No explicit Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com